Translation:I eat lunch.
As others have commented, the お here is an honorific and is not a necessary part of the word.
However, I have to disagree with all the comments about it indicating whose food is being referred to. In many cases, like お名前, the use of お does indicate respect for the listener (and hence the word's directionality), but there is a subset of keigo known as 美化語 (bikago = "beautification speech"). https://en.wikipedia.org/wiki/Honorific_speech_in_Japanese#Word_beautification
As it says in the article, sometimes Japanese people make their speech polite for politeness' sake because it sounds nicer, classier, or more "beautiful". In some cases (such as this sentence), the お (or ご) honorific is used withouth the speaker being intentionally deferential to the listener.
The most common case of this is お茶. You will almost never hear a Japanese person refer to tea, their own or anyone else's, as simply 茶 (unless it is part of another word like 抹茶 maccha or ウーロン茶 uuroncha). The word 茶 has been "beautified" so much in Japanese culture, that to say it without the お sounds crass or rough.
But why lunch? There isn't an お in 晩御飯 or 朝御飯. unless you mean ご... On a related topic, my IME automatically did full kanji on the first one, but not on 朝.
In this case, it gives you a clue as to who's doing the eating. You probably wouldn't use the honorific お for your own food, because that would be presumptuous, so its inclusion is what resolves the "I eat lunch"/"you eat lunch" ambiguity.
So does this mean that お昼ご飯を食べます should rather be translated as 'You are eating lunch'?
No. Your sentence is using the progressive verb tense, while this sentence is in polite non-past.
No, お I think is a way of making something polite like お名前 is 'your honerable name'. It doesnt have to be there though however im not sure can someome confirm this?
Yes, putting "o" in front of something is a way of making it polite, like calling something an "honorable--" whatever. It can go in front of most nouns, though admittedly calling something an "honorable desk" would be weird, so it's not always used.
Could it also sometimes come across as sarcastic, and perhaps offensive if used to refer to a person without a sincere tone, or am I overthinking things?
From my studies, をis also used as a marker of what a verb acts upon. This is the case
I was told that women use the お honorific when referring to food, men usually skip it.
Can it be translated into 'Let's eat lunch' because it appears that the sayer is talking to another person? Also 'O' is not normally referring my own lunch. Quite confused
No. You would have to use tabemashou "let's eat/shall we eat" conjugation.
It seems to be speaking in more of a general sense rather than something that you will do in the future. Although in the right context, I think you could use it to mean "I will eat lunch" but for a more direct translation the "will" should be left out. I'm no native Japanese speaker though so I could be wrong
I think -- but I could be wrong -- that to say that you will eat "the lunch" you would need to topicalize it with a は, like in those "I don't eat X" sentences some lessons ago. A simple "I will eat lunch" (without the "the") should be correct, however. Duolingo can be a bit picky about your English, so whenever you get a surprising "Wrong answer!" the first thing to do should be to check if you slipped up in your English grammar. :)
TWICE I got this wrong because i accidentally chose "eight" instead of "eat" ಠ_ಠ
Of course 'I eat lunch.' is correct but pressing 'I' does not work. The 'I' button is dead.
This is 'I eat lunch.' or 'I will eat lunch'. because Japanese has no future tense. The initial o is used as a term of respect to a senior person or a superior. This has nothing to do with whose lunch is involved.